45 questions. Try each one, then open the answer to check yourself and read the explanation.
Two cars moving in the same direction have speeds of 100 kmh−1 and 130 kmh−1. What is the velocity of the faster car as measured by an observer in the slower car?
Answer: D (30kmh−1)
For bodies moving in the same direction, the relative velocity is the difference of their speeds: 130 − 100 = 30 km h−1.
The diagram above shows a velocity-time graph. The statement that is true about this motion is that, the car
Answer: D (has no acceleration between point F and G.)
Between F and G the graph is horizontal, so the velocity does not change and the acceleration is zero. E to F is acceleration and G to H is deceleration.
A stone and a feather are dropped from the same height above the earth surface. Ignoring air resistance, which of the following is correct?
Answer: A (The stone and feather will both reach the ground at the same time)
Without air resistance every body falls with the same acceleration g, whatever its mass, so both land together.
A car moves with an initial velocity of 25 ms−1 and reaches a velocity of 45 ms−1 in 10s. What is the acceleration of the car?
Answer: D (2 ms−2)
a = (v − u)/t = (45 − 25) ÷ 10 = 2 m s−2.
An object is weighed at different locations on the earth. What will be the right observation?
Answer: C (The mass is constant while the weight varies)
Mass (amount of matter) does not change, but weight = mg, and g varies slightly from place to place on the earth, so weight varies.
The diagram above represents balls in an undulating surface. Which of the following options represents positions of stable equilibrium?
Answer: C (III, VI and IX)
A ball resting in a hollow (trough) returns there if displaced, so it is in stable equilibrium. Balls iii, vi and ix sit in the troughs.
A bob of weight 0.1 N hangs from a massless string of length 50 cm. A variable horizontal force which increases from zero is applied to pull the bob until the string makes an angle of 60° with the vertical. The work done is
Answer: B (0.025 J.)
The bob rises h = L(1 − cos 60°) = 0.5 × 0.5 = 0.25 m. Work done = gain in potential energy = 0.1 × 0.25 = 0.025 J.
The surfaces of conveyor belts are made rough so as to
Answer: A (prevent the load from slipping.)
A rough surface increases friction between the belt and the load, so the load does not slip.
A machine of velocity ratio 6 requires an effort of 400 N to raise a load of 800 N through 1 m. Find the efficiency of the machine.
Answer: C (33.3%.)
MA = 800 ÷ 400 = 2. Efficiency = MA/VR × 100% = 2/6 × 100% ≈ 33.3%.
If a wire 30 cm long is extended to 30.5 cm by a force 300 N. Find the strain energy of the wire.
Answer: D (0.75 J.)
Extension = 0.5 cm = 0.005 m. Strain energy = ½Fe = ½ × 300 × 0.005 = 0.75 J.
In a hydraulic press, the pump piston exerts a pressure of 100 Pa on the liquid. What force is exerted in the second piston of cross-sectional area 3 m2?
Answer: D (300 N)
Pressure is transmitted equally through the liquid, so F = pA = 100 × 3 = 300 N.
The accurate measurement of the relative density of a substance in its powdered form is done with a beam balance and
Answer: D (a density bottle.)
A density (specific gravity) bottle holds a fixed volume exactly, so it is used with a balance to find the relative density of powders and granules.
A hydrometer is an instrument used in measuring
Answer: B (relative density of a liquid.)
A hydrometer floats in a liquid and the depth it sinks to shows the liquid's relative density, read off its scale.
One special advantage of alcohol over mercury as a thermometric liquid is its
Answer: A (low freezing point.)
Mercury freezes at −39°C, but alcohol stays liquid down to about −115°C, so alcohol thermometers can be used in very cold places.
Two metals P and Q of lengths l1 and l2 are heated through the same temperature difference. If the ratio of the linear expansivities of P to Q is 2:3 and the ratio of their lengths is 3:4. What is the ratio of increase in lengths of P to Q?
Answer: C (1:2)
Increase in length = αlΔθ. Ratio = (2/3) × (3/4) = 1/2, so 1 : 2.
The density of a certain oil on frying becomes 0.4 kgm−3 with a volume of 20 m3. What will be its initial volume when its initial density is 0.8 kgm−3 assuming no loss of oil due to spillage?
Answer: A (10 kgm−3)
Mass = density × volume = 0.4 × 20 = 8 kg, and the mass does not change. Initial volume = 8 ÷ 0.8 = 10 m3.
Heat is radiated by all hot objects in the form of
Answer: C (infrared rays.)
Hot bodies give out radiant heat mainly as infrared radiation, an electromagnetic wave just beyond red light.
If a container is filled with ice to the brim, what happens to the level of water when the ice completely melts?
Answer: B (The level of water drops)
Ice is less dense than water, so the same mass of water takes up less volume after melting. The level falls below the brim.
The small droplet of water that forms on the grass in the early hours of the morning is
Answer: A (dew.)
At night the grass cools below the dew point and water vapour condenses on it as droplets called dew.
The pressure of one mole of an ideal gas of volume 10−2m3 at a temperature of 27°C is [Molar gas constant = 8.3 J mol−1K−1]
Answer: C (2.49 × 105 Nm−1.)
P = nRT/V = 1 × 8.3 × 300 ÷ 10−2 = 2.49 × 105 N m−2.
Which of the following has no effect on radiation?
Answer: A (density)
The rate of radiation depends on the body's temperature, its surface area and the nature of its surface (dull black radiates best), not on its density.
The wavelength of a wave travelling with a velocity of 420 ms−1 is 42 m. What is its period?
Answer: B (0.1 s)
f = v/λ = 420 ÷ 42 = 10 Hz, so the period T = 1/f = 0.1 s.
The sound of an electric bell dies down slowly when air is slowly pumped out from a bottle because
Answer: C (sound needs a material medium.)
As air is removed there is less medium to carry the vibrations, so the sound fades. Sound needs a material medium and cannot travel through a vacuum.
During a thunderstorm, the sound is heard over a long time. This phenomenon is referred to as
Answer: B (reverberation)
The thunder is reflected many times by clouds, hills and buildings, and these overlapping reflections make the sound last a long time: reverberation (rolling of thunder).
The velocity of sound in air at 16°C is 340ms−1. What will it be when the pressure is doubled and its temperature raised to 127°C?
Answer: D (400ms−1)
Pressure has no effect on the speed of sound; v ∝ √T (kelvin). v = 340 × √(400/289) = 340 × 20/17 = 400 m s−1.
In comparing the camera and the human eye, the film of the camera functions as the
Answer: D (retina.)
The image in a camera is formed on the film; in the eye it is formed on the retina. So the film corresponds to the retina.
An object 4cm high is placed 15cm from a concave mirror of local length 5cm. The size of the image is
Answer: D (2cm.)
1/v = 1/5 − 1/15 = 2/15, so v = 7.5 cm. Image height = object height × v/u = 4 × 7.5/15 = 2 cm.
An object is embedded in a block of ice, 10 cm below the plane surface. If the refractive index of the ice is 1.50, the apparent depth of the object below the surface is
Answer: A (6.77 cm.)
Apparent depth = real depth ÷ refractive index = 10 ÷ 1.5 ≈ 6.67 cm, which is option A.
Which of the following is used for the correction of short-sightedness?
Answer: A (Concave lens)
A short-sighted eye focuses distant light in front of the retina. A diverging (concave) lens spreads the light so it focuses on the retina.
Dispersion occurs when white light passes through a glass prism because of the
Answer: A (different speeds of the colours in the glass.)
Each colour travels at a slightly different speed in glass, so each is refracted by a different amount and white light spreads into a spectrum.
When a positively charged rod is brought nearer the cap of a positively charged electroscope, the leaves' divergence will
Answer: C (diverge.)
The positive rod repels positive charge from the cap down to the leaves, so the leaves carry more charge and diverge further.
Three capacitors of capacitance, 2μF, 4μF and 8μF are connected in parallel and a p.d of 6 V is maintained across each capacitor, the total energy stored is
Answer: C (2.52 × 10−4 J.)
In parallel C = 2 + 4 + 8 = 14 μF. Energy = ½CV2 = ½ × 14 × 10−6 × 62 = 2.52 × 10−4 J.
A cell of emf 12 V and internal resistance 4Ω is connected to an external resistor of resistance 2Ω. Find the current flow.
Answer: B (2 A.)
I = E/(R + r) = 12 ÷ (2 + 4) = 2 A.
Three 4Ω resistors connected in parallel have a potential difference of 16 V applied across them. What is the total current in the circuit?
Answer: A (12 A)
Three 4 Ω resistors in parallel give 4/3 Ω. I = V/R = 16 ÷ (4/3) = 12 A (4 A through each resistor).
In the diagram above, a 200 W bulb is lighted by a 240 V a.c mains supply. If 1kWh is sold at ₦40, the cost of keeping the bulb lighted for a day is
Answer: A (₦192.00.)
Energy in a day = 0.2 kW × 24 h = 4.8 kWh. Cost = 4.8 × ₦40 = ₦192.00.
Power supply is transmitted at a very high voltage and low current in order to
Answer: B (prevent overheating of the coil.)
Heat lost in the cables is I2R. Using a small current (at high voltage) cuts this heating and the energy wasted.
In the diagram above, if the south-poles of two magnets stroke a steel bar, the polarities at T and V will respectively be
Answer: C (north and north.)
In the divided-touch method, each end of the bar where the stroke finishes gets the opposite polarity to the stroking pole. Both S poles finish at the ends T and V, so both become north poles.
A galvanometer with full-scale deflection of 10 mA is to be converted to a voltmeter with full-scale deflection of 5 V. If a series resistance of 498Ω is used for the conversion, the resistance of the galvanometer is
Answer: A (2 Ω.)
At full scale V = I(Rg + R): 5 = 0.01 × (Rg + 498), so Rg + 498 = 500 and Rg = 2 Ω.
In alternating current circuit at resonance, the angle of lead or lag is
Answer: B (0°)
At resonance the inductive and capacitive reactances cancel, leaving only resistance. Current and voltage are in phase, so the phase angle is 0°.
In Faraday's law of electrolysis, a graph of mass deposited against the quantity of electricity is plotted. The slope of the graph gives
Answer: A (the electrochemical equivalent.)
Faraday's first law: m = zQ. A graph of m against Q is a straight line of slope z, the electrochemical equivalent.
In a discharge tube, most of the gas is pumped out so that electricity is conducted at
Answer: B (low pressure.)
Gases conduct electricity well only at low pressure (with a high voltage), so most of the gas is pumped out of a discharge tube.
The radioisotope 23592U decays by emitting two alpha particles, three beta particles and a gamma ray. What is the mass and atomic numbers of the resulting daughter element?
Answer: C (227 and 91)
Two alphas remove 8 from the mass number and 4 from the atomic number; three betas add 3 to the atomic number; gamma changes neither. Mass number = 235 − 8 = 227, atomic number = 92 − 4 + 3 = 91.
Transistors are used for the
Answer: C (amplification of signals.)
A small base current controls a much larger collector current, so a transistor amplifies signals. Rectification is done by diodes.
A typical transistor characteristic is represented as
Answer: D (D)
The output characteristic of a transistor (collector current against collector voltage) rises quickly at first and then becomes almost flat, as in graph D.
Which of the following is a pure semiconductor?
Answer: A (Silicon)
Pure (intrinsic) silicon is a semiconductor. Phosphorus is a doping impurity and a transistor is a device, not a material.